CN105372706A - Seismic oscillation amplitude modulation index and amplitude modulation coefficient evaluation method - Google Patents

Abstract

The invention relates to a seismic oscillation amplitude modulation index and amplitude modulation coefficient evaluation method. The objective of the invention is to solve the defect of large introduced errors in quantitative evaluation of seismic oscillation amplitude modulation in the earthquake engineering field in the prior art. An amplitude modulation index and amplitude modulation coefficient evaluation method which is capable of quantitatively evaluating seismic oscillation does not exist in the prior art. The seismic oscillation amplitude modulation index and amplitude modulation coefficient evaluation method of the invention has the following steps that: step one, inelastic SDOF structure dynamic characteristics are determined; step two, eight seismic oscillation parameters are selected as amplitude modulation indexes; step three, unmodulated seismic oscillation records are adopted to calculate a correlation coefficient between structural reaction and the amplitude modulation indexes through utilizing the inelastic SDOF structure dynamic characteristics determined in the step one and the eight seismic oscillation parameters which are obtained in step two; step four, modulated seismic oscillation records are adopted to calculate a correlation coefficient between the structural reaction and the amplitude modulation indexes through utilizing the inelastic SDOF structure dynamic characteristics determined in the step one and the eight seismic oscillation parameters which are obtained in step two; and step five, the ratio of the correlation coefficient obtained in the step four and the correlation coefficient obtained in the step three is calculated, and the more the ratio approaches to 1.0, the smaller errors introduced by seismic oscillation amplitude modulation are. The seismic oscillation amplitude modulation index and amplitude modulation coefficient evaluation method of the invention is applied to the earthquake engineering field.

Description

A kind of earthquake motion amplitude modulation index and amplitude modulation coefficient assessment method

Technical field

The present invention relates to earthquake motion amplitude modulation index and amplitude modulation coefficient assessment method.

Background technology

Along with the develop rapidly of day by day maturation and the operational speed of a computer of structure analysis software, the Nonlinear dynamic analysis analysis of structure develops into a kind of main research means in earthquake engineering gradually.When carrying out nonlinear dynamical damage to structure, need to choose suitable amplitude modulation index and amplitude modulation coefficient by earthquake motion amplitude modulation to the seismic risk level in place, structure place, this has just related to the amplitude modulation problem of earthquake motion.

Up to the present, the common practice of earthquake motion amplitude modulation first selects some ground motion parameters as amplitude modulation index, then earthquake motion is multiplied by (or divided by) amplitude modulation coefficient and makes it reach given seismic risk level.In order to reduce the seismic analysis error brought because of earthquake motion amplitude modulation, needing to select appropriate amplitude modulation index and amplitude modulation coefficient in actual applications, making the earthquake motion after amplitude modulation can reflect the damage potential shaken practically.But, also do not have ripe method can evaluate amplitude modulation index and the amplitude modulation coefficient of earthquake motion quantitatively at present.Therefore, a kind of method of necessary proposition carrys out the seismic analysis error that quantitative evaluation is taked to bring when certain amplitude modulation index and amplitude modulation coefficient.

Summary of the invention

The object of the invention is to solve quantitative assessment earthquake motion error that amplitude modulation is introduced in existing earthquake engineering field large, also do not propose a kind ofly to evaluate the amplitude modulation index of earthquake motion and the problem of amplitude modulation coefficient method quantitatively, and propose a kind of earthquake motion amplitude modulation index and amplitude modulation coefficient assessment method.

Above-mentioned goal of the invention is achieved through the following technical solutions:

Step one, determine non-resilient SDOF structural dynamic characteristic, non-resilient SDOF structural dynamic characteristic comprises cycle, damping ratio, hysteretic characteristic and intensity, and SDOF is single-degree-of-freedom;

Step 2, choosing 8 ground motion parameters as amplitude modulation index, is peak ground acceleration (PGA), peak ground speed (PGV), peak ground displacement (PGD), Arias earthquake intensity (I respectively _a), Park-Ang characteristic strength (I _c), Housner earthquake intensity (d _rms), spectral acceleration (S _a) and Housner spectrum intensity (S _i);

8 amplitude modulation indexs that step 3, the non-resilient SDOF structural dynamic characteristic utilizing step one to determine and step 2 are chosen, adopt the related coefficient between the reaction of non-amplitude modulation seismic motion record computation structure with amplitude modulation index;

8 amplitude modulation indexs that step 4, the non-resilient SDOF structural dynamic characteristic utilizing step one to determine and step 2 are chosen, adopt the related coefficient between the reaction of amplitude modulation seismic motion record computation structure and amplitude modulation index;

Ratio between the related coefficient that step 5, calculation procedure four obtain and the related coefficient that step 3 obtains, this ratio more levels off to 1.0, shows that the error that earthquake motion amplitude modulation is introduced is less.

Invention effect

Adopt the assessment technology of earthquake motion amplitude modulation index of the present invention and amplitude modulation coefficient, to solve in earthquake engineering field quantitative assessment earthquake motion amplitude modulation introduce the large problem of error.The amplitude modulation of earthquake motion is not only relevant with the characteristic of amplitude modulation index, also relevant with the size of amplitude modulation coefficient, existing technology only considers the characteristic of amplitude modulation index, and amplitude modulation index is combined with amplitude modulation coefficient by the method for damage potential to structures by the assessment technology that this patent proposes, and then the impact of amplitude modulation index properties and amplitude modulation coefficient size can be considered when weighing the error that earthquake motion amplitude modulation is introduced.Because existing technology only considers the characteristic of amplitude modulation index, can more than 30% be reached to the evaluated error of earthquake motion amplitude modulation; And the art of this patent considers the impact of amplitude modulation index properties and amplitude modulation coefficient size, thus evaluated error can be controlled within 15%.When using this achievement, very simple and practical, the quality of evaluation amplitude modulation index directly perceived and quantitative and amplitude modulation coefficient is directly got final product according to the result provided.This method is simple simultaneously, also simply can be applied to other structural models and amplitude modulation index.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention, ρ _unscaledfor the related coefficient that non-amplitude modulation earthquake motion is corresponding, ρ _scaledfor the related coefficient that amplitude modulation earthquake motion is corresponding;

Fig. 2 is related coefficient ratio ρ _{amplitude modulation}/ ρ _{non-amplitude modulation}with the graph of a relation of earthquake motion amplitude modulation coefficient SF, ρ (DM, S _a) be structural response DM and amplitude modulation index S _abetween related coefficient, DM is structural response, S _afor spectral acceleration, x _maxfor structure maximum displacement response, E _hfor hysteretic energy of structures reaction;

Fig. 3 is related coefficient ratio ρ _{amplitude modulation}/ ρ _{non-amplitude modulation}with the graph of a relation of earthquake motion amplitude modulation coefficient SF, ρ (DM, PGA) is the related coefficient between structural response DM and amplitude modulation index PGA, and PGA is peak ground acceleration;

Fig. 4 is related coefficient ratio ρ _{amplitude modulation}/ ρ _{non-amplitude modulation}with the graph of a relation of earthquake motion amplitude modulation coefficient SF, ρ (DM, I _a) be structural response DM and amplitude modulation index I _abetween related coefficient, I _afor Arias earthquake intensity;

Fig. 5 is related coefficient ratio ρ _{amplitude modulation}/ ρ _{non-amplitude modulation}with the graph of a relation of earthquake motion amplitude modulation coefficient SF, ρ (DM, I _c) be structural response DM and amplitude modulation index I _cbetween related coefficient, I _cfor Park-Ang characteristic strength;

Fig. 6 is related coefficient ratio ρ _{amplitude modulation}/ ρ _{non-amplitude modulation}with the graph of a relation of earthquake motion amplitude modulation coefficient SF, ρ (DM, S _i) be structural response DM and amplitude modulation index S _ibetween related coefficient, S _ifor Housner spectrum intensity, Housner is Hao Sina;

Fig. 7 is related coefficient ratio ρ _{amplitude modulation}/ ρ _{non-amplitude modulation}with the graph of a relation of earthquake motion amplitude modulation coefficient SF, ρ (DM, PGV) is the related coefficient between structural response DM and amplitude modulation index PGV, and PGV is peak ground speed;

Fig. 8 is related coefficient ratio ρ _{amplitude modulation}/ ρ _{non-amplitude modulation}with the graph of a relation of earthquake motion amplitude modulation coefficient SF, ρ (DM, d _rms) be structural response DM and amplitude modulation index d _rmsbetween related coefficient, d _rmsfor Housner earthquake intensity, Housner is Hao Sina;

Fig. 9 is related coefficient ratio ρ _{amplitude modulation}/ ρ _{non-amplitude modulation}with the graph of a relation of earthquake motion amplitude modulation coefficient SF, ρ (DM, PGD) is the related coefficient between structural response DM and amplitude modulation index PGD, and PGD is peak ground displacement.

Embodiment

Embodiment one: composition graphs 1 illustrates present embodiment, a kind of earthquake motion amplitude modulation index of present embodiment and amplitude modulation coefficient assessment method, specifically prepare according to following steps:

Step one, determine non-resilient SDOF structural dynamic characteristic, non-resilient SDOF structural dynamic characteristic comprises cycle, damping ratio, hysteretic characteristic and intensity, and SDOF is single-degree-of-freedom;

Step 2, choosing 8 ground motion parameters as amplitude modulation index, is peak ground acceleration (PGA), peak ground speed (PGV), peak ground displacement (PGD), Arias earthquake intensity (I respectively _a), Park-Ang characteristic strength (I _c), Housner earthquake intensity (d _rms), spectral acceleration (S _a) and Housner spectrum intensity (S _i);

8 amplitude modulation indexs that step 3, the non-resilient SDOF structural dynamic characteristic utilizing step one to determine and step 2 are chosen, adopt the related coefficient between the reaction of non-amplitude modulation seismic motion record computation structure with amplitude modulation index;

8 amplitude modulation indexs that step 4, the non-resilient SDOF structural dynamic characteristic utilizing step one to determine and step 2 are chosen, adopt the related coefficient between the reaction of amplitude modulation seismic motion record computation structure and amplitude modulation index;

Ratio between the related coefficient that step 5, calculation procedure four obtain and the related coefficient that step 3 obtains, this ratio more levels off to 1.0, shows that the error that earthquake motion amplitude modulation is introduced is less.As Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8 and Fig. 9.

Embodiment two: present embodiment and embodiment one unlike: determine non-resilient SDOF architectural characteristic in described step one, non-resilient SDOF architectural characteristic comprises cycle, damping ratio, hysteretic characteristic and intensity; Detailed process is:

The periodic regime of non-resilient SDOF structure is 0.1 ~ 6.0s, period distances is 0.1s, assuming that the damping ratio of non-resilient SDOF structure is 5%, adopt the hysteretic characteristic of the non-resilient SDOF structure of ideal elastic-plastic (EPP) modeling, the lateral strength of non-resilient SDOF structure is weighed by strength reduction factor R, formula (1) is shown in the definition of R, and the value of R is set as 2,4,6;

The computing formula of strength reduction factor R is:

$R=\frac{F_e}{F_y}---\left(1\right)$

Wherein, F _erepresent that elasticity SDOF structural system keeps the minimum intensity required for elasticity under given earthquake motion effect, and F _yrepresent the yield strength of non-resilient SDOF structure.

Other step and parameter identical with embodiment one.

Embodiment three: present embodiment and embodiment one or two, unlike 8 amplitude modulation indexs that the non-resilient SDOF structural dynamic characteristic utilizing step one to determine in described step 3 and step 2 are chosen, adopt non-amplitude modulation seismic motion record computation structure to react related coefficient between the amplitude modulation index; Detailed process is:

The process adopting non-amplitude modulation seismic motion record computation structure to react is:

Choose 364 seismic motion record, the non-resilient SDOF structural dynamic characteristic determined according to step one calculates the maximum displacement response value of non-resilient SDOF structure under non-amplitude modulation earthquake motion effect and hysteretic energy reacting value:

$m\stackrel{\·\·}{v}+c\stackrel{\·}{v}+f_s=-m{\stackrel{\·\·}{v}}_g---\left(2\right)$

Wherein, m is non-resilient SDOF architecture quality, and c is non-resilient SDOF structure viscous damping coefficient, f _sfor non-resilient SDOF structure recovery power, for the second derivative of v, i.e. the acceleration response of non-resilient SDOF structure, for the first order derivative of v, i.e. the speed responsing of non-resilient SDOF structure, v is relative displacement, for v _gsecond derivative, i.e. earthquake ground motion acceleration, v _gfor seismic displacement;

The maximal value of relative displacement time-histories is maximum displacement response value, and hysteretic energy reacting value obtains by carrying out integral and calculating to relative displacement time-histories and restoring force time-histories, and earthquake motion finish time, corresponding integrated value was hysteretic energy reacting value;

The process of the related coefficient adopting non-amplitude modulation seismic motion record computation structure to react between amplitude modulation index is:

For any two vectorial X and Y, correlation coefficient value between the two can be calculated as follows:

$\mathrm{\ρ}(X,Y)=\frac{n\mathrm{\Σ}(X\·Y)-\mathrm{\Σ}X\·\mathrm{\Σ}Y}{\sqrt{(n\mathrm{\Σ}{\left(X\right)}^2-{\left(\mathrm{\Σ}X\right)}^2)\·(n\mathrm{\Σ}{\left(Y\right)}^2-{\left(\mathrm{\Σ}Y\right)}^2)}}---\left(3\right)$

Wherein n is earthquake motion number, vectorial X is set to the structural response value under 364 non-amplitude modulation earthquake motion effects, i.e. maximum displacement response or hysteretic energy reaction, and amplitude modulation Y being set to 364 non-amplitude modulation earthquake motions corresponding refers to target value;

Periodic regime 0.1 ~ 6.0s is divided into three constant time ranges, be respectively short period section 0.1 ~ 0.5s, medium constant time range 0.6 ~ 1.5s and long period section 1.6 ~ 6.0s, first calculate related coefficient corresponding to each constant time range respectively, then the weighting coefficient of three constant time ranges is weighted and on average obtains weighted mean related coefficient be the related coefficient between structural response and amplitude modulation index, by following formulae discovery:

${\stackrel{\‾}{\mathrm{\ρ}}}_w=\frac{1}{n_1\·n_2}{\mathrm{\Σ\ρ}}_{ij}\·w_j---\left(4\right)$

Wherein ρ _ijfor i-th strength reduction factor calculating according to formula (3) and related coefficient corresponding to a jth structural cycle, n ₁for the number of strength reduction factor R, n ₂for the number of free vibration period of structure T, w _jfor the weight coefficient of a jth free vibration period of structure, i span is 1 ~ n ₁, j span is 1 ~ n ₂, n ₁span is 1 ~ 6, n ₂span is 30 ~ 100.

Other step and parameter identical with embodiment one or two.

Embodiment four: one of present embodiment and embodiment one to three, unlike 8 amplitude modulation indexs that the non-resilient SDOF structural dynamic characteristic utilizing step one to determine in described step 4 and step 2 are chosen, adopt the related coefficient between the reaction of amplitude modulation seismic motion record computation structure with amplitude modulation index; Detailed process is;

The process adopting amplitude modulation seismic motion record computation structure to react is:

Choose 364 seismic motion record, after selecting amplitude modulation index and amplitude modulation coefficient, selected amplitude modulation coefficient is multiplied by each seismic motion record and is the seismic motion record after amplitude modulation, the value of amplitude modulation coefficient is the positive integer of 1.0-10.0, and the non-resilient SDOF structural dynamic characteristic determined according to step one calculates the maximum displacement response value of non-resilient SDOF structure under amplitude modulation earthquake motion effect and hysteretic energy reacting value;

$m\stackrel{\·\·}{v}+c\stackrel{\·}{v}+f_s=-m{\stackrel{\·\·}{v}}_g---\left(2\right)$

Wherein, m is non-resilient SDOF architecture quality, and c is non-resilient SDOF structure viscous damping coefficient, f _sfor non-resilient SDOF structure recovery power, for the second derivative of v, i.e. the acceleration response of non-resilient SDOF structure, for the first order derivative of v, i.e. the speed responsing of non-resilient SDOF structure, v is relative displacement, for v _gsecond derivative, i.e. earthquake ground motion acceleration, v _gfor seismic displacement;

The maximal value of relative displacement is maximum displacement response value, and hysteretic energy reacting value obtains by carrying out integral and calculating to relative displacement time-histories and restoring force time-histories, and earthquake motion finish time, corresponding integrated value was hysteretic energy reacting value;

The process of the related coefficient adopting amplitude modulation seismic motion record computation structure to react between amplitude modulation index is:

For any two vectorial X and Y, correlation coefficient value between the two can be calculated as follows:

$\mathrm{\ρ}(X,Y)=\frac{n\mathrm{\Σ}(X\·Y)-\mathrm{\Σ}X\·\mathrm{\Σ}Y}{\sqrt{(n\mathrm{\Σ}{\left(X\right)}^2-{\left(\mathrm{\Σ}X\right)}^2)\·(n\mathrm{\Σ}{\left(Y\right)}^2-{\left(\mathrm{\Σ}Y\right)}^2)}}---\left(3\right)$

Wherein n is earthquake motion number, vectorial X is set to the structural response value under 364 non-amplitude modulation earthquake motion effects, i.e. maximum displacement response or hysteretic energy reaction, and amplitude modulation Y being set to 364 non-amplitude modulation earthquake motions corresponding refers to target value;

Periodic regime 0.1-6.0s is divided into three constant time ranges, be respectively short period section (0.1-0.5s), medium cycle short (0.6-1.5s) and long period section (1.6-6.0s), first calculate related coefficient corresponding to each cycle respectively, then the weighting coefficient of three constant time ranges is weighted and on average obtains weighted mean related coefficient be the related coefficient between structural response and amplitude modulation index, by following formulae discovery:

${\stackrel{\‾}{\mathrm{\ρ}}}_w=\frac{1}{n_1\·n_2}{\mathrm{\Σ\ρ}}_{ij}\·w_j---\left(4\right)$

Wherein ρ _ijby according to formula (3) calculating i-th strength reduction factor and related coefficient corresponding to a jth structural cycle, n ₁for the number of strength reduction factor R, n ₂for the number of free vibration period of structure T, w _jfor the weight coefficient of a jth free vibration period of structure.

Other step and parameter identical with one of embodiment one to three.

Embodiment five: one of present embodiment and embodiment one to four unlike: the weighting coefficient of described three constant time ranges is short period section is 4, and medium constant time range is 2, and long period section is 4/9.

Other step and parameter identical with one of embodiment one to four.

Claims (5)

1. earthquake motion amplitude modulation index and an amplitude modulation coefficient assessment method, is characterized in that what a kind of earthquake motion amplitude modulation index and amplitude modulation coefficient assessment method specifically carried out according to following steps:

Step one, determine non-resilient SDOF structural dynamic characteristic, non-resilient SDOF structural dynamic characteristic comprises cycle, damping ratio, hysteretic characteristic and intensity, and SDOF is single-degree-of-freedom;

Step 2, choosing 8 ground motion parameters as amplitude modulation index, is peak ground acceleration, peak ground speed, peak ground displacement, Arias earthquake intensity, Park-Ang characteristic strength, Housner earthquake intensity, spectral acceleration and Housner spectrum intensity respectively;

8 amplitude modulation indexs that step 3, the non-resilient SDOF structural dynamic characteristic utilizing step one to determine and step 2 are chosen, adopt the related coefficient between the reaction of non-amplitude modulation seismic motion record computation structure with amplitude modulation index;

8 amplitude modulation indexs that step 4, the non-resilient SDOF structural dynamic characteristic utilizing step one to determine and step 2 are chosen, adopt the related coefficient between the reaction of amplitude modulation seismic motion record computation structure and amplitude modulation index;

Ratio between the related coefficient that step 5, calculation procedure four obtain and the related coefficient that step 3 obtains, this ratio more levels off to 1.0, shows that the error that earthquake motion amplitude modulation is introduced is less.

2. a kind of earthquake motion amplitude modulation index and amplitude modulation coefficient assessment method according to claim 1, it is characterized in that: in described step one, determine non-resilient SDOF architectural characteristic, non-resilient SDOF architectural characteristic comprises cycle, damping ratio, hysteretic characteristic and intensity, and SDOF is single-degree-of-freedom; Detailed process is:

The periodic regime of non-resilient SDOF structure is 0.1-6.0s, period distances is 0.1s, assuming that the damping ratio of non-resilient SDOF structure is 5%, ideal elastoplastic model is adopted to simulate the hysteretic characteristic of non-resilient SDOF structure, the intensity of non-resilient SDOF structure is weighed by strength reduction factor R, formula (1) is shown in the definition of R, and the value of R is set as 2,4,6;

The computing formula of strength reduction factor R is:

$R=\frac{F_e}{F_y}---\left(1\right)$

Wherein, F _erepresent that elasticity SDOF structural system keeps the minimum intensity required for elasticity under given earthquake motion effect, and F _yrepresent the yield strength of non-resilient SDOF structure.

3. a kind of earthquake motion amplitude modulation index and amplitude modulation coefficient assessment method according to claim 2, it is characterized in that: 8 amplitude modulation indexs that the non-resilient SDOF structural dynamic characteristic utilizing step one to determine in described step 3 and step 2 are chosen, adopt the related coefficient between the reaction of non-amplitude modulation seismic motion record computation structure with amplitude modulation index; Detailed process is:

The process adopting non-amplitude modulation seismic motion record computation structure to react is:

Choose 364 seismic motion record, the non-resilient SDOF structural dynamic characteristic determined according to step one calculates the maximum displacement response value of non-resilient SDOF structure under non-amplitude modulation earthquake motion effect and hysteretic energy reacting value:

$m\stackrel{\·\·}{v}+c\stackrel{\·}{v}+f_s=-m{\stackrel{\·\·}{v}}_g---\left(2\right)$

Wherein, m is non-resilient SDOF architecture quality, and c is non-resilient SDOF structure viscous damping coefficient, f _sfor non-resilient SDOF structure recovery power, for the second derivative of v, i.e. the acceleration response of non-resilient SDOF structure, for the first order derivative of v, i.e. the speed responsing of non-resilient SDOF structure, v is relative displacement, for v _gsecond derivative, i.e. earthquake ground motion acceleration, v _gfor seismic displacement;

The maximal value of relative displacement time-histories is maximum displacement response value, and hysteretic energy reacting value obtains by carrying out integral and calculating to relative displacement time-histories and restoring force time-histories, and earthquake motion finish time, corresponding integrated value was hysteretic energy reacting value;

The process of the related coefficient adopting non-amplitude modulation seismic motion record computation structure to react between amplitude modulation index is:

For any two vectorial X and Y, correlation coefficient value between the two can be calculated as follows:

$\mathrm{\ρ}(X,Y)=\frac{n\mathrm{\Σ}(X\·Y)-\mathrm{\Σ}X\·\mathrm{\Σ}Y}{\sqrt{(n\mathrm{\Σ}{\left(X\right)}^2-{\left(\mathrm{\Σ}X\right)}^2)\·(n\mathrm{\Σ}{\left(Y\right)}^2-{\left(\mathrm{\Σ}Y\right)}^2)}}---\left(3\right)$

Wherein n is earthquake motion number, vectorial X is set to the structural response value under 364 non-amplitude modulation earthquake motion effects, i.e. maximum displacement response or hysteretic energy reaction, and amplitude modulation Y being set to 364 non-amplitude modulation earthquake motions corresponding refers to target value;

Periodic regime 0.1 ~ 6.0s is divided into three constant time ranges, be respectively short period section 0.1 ~ 0.5s, medium constant time range 0.6 ~ 1.5s and long period section 1.6 ~ 6.0s, first calculate related coefficient corresponding to each constant time range respectively, then the weighting coefficient of three constant time ranges is weighted and on average obtains weighted mean related coefficient be the related coefficient between structural response and amplitude modulation index, by following formulae discovery:

${\stackrel{\‾}{\mathrm{\ρ}}}_w=\frac{1}{n_1\·n_2}{\mathrm{\Σ\ρ}}_{ij}\·w_j---\left(4\right)$

Wherein ρ _ijfor i-th strength reduction factor calculating according to formula (3) and related coefficient corresponding to a jth structural cycle, n ₁for the number of strength reduction factor R, n ₂for the number of free vibration period of structure T, w _jfor the weight coefficient of a jth free vibration period of structure, i span is 1 ~ n ₁, j span is 1 ~ n ₂, n ₁span is 1 ~ 6, n ₂span is 30 ~ 100.

4. a kind of earthquake motion amplitude modulation index and amplitude modulation coefficient assessment method according to claim 3, it is characterized in that: 8 amplitude modulation indexs that the non-resilient SDOF structural dynamic characteristic utilizing step one to determine in described step 4 and step 2 are chosen, adopt the related coefficient between the reaction of amplitude modulation seismic motion record computation structure and amplitude modulation index; Detailed process is;

The process adopting amplitude modulation seismic motion record computation structure to react is:

Choose 364 seismic motion record, after selecting amplitude modulation index and amplitude modulation coefficient, selected amplitude modulation coefficient is multiplied by each seismic motion record and is the seismic motion record after amplitude modulation, the value of amplitude modulation coefficient is the positive integer of 1.0-10.0, and the non-resilient SDOF structural dynamic characteristic determined according to step one calculates the maximum displacement response value of non-resilient SDOF structure under amplitude modulation earthquake motion effect and hysteretic energy reacting value;

$m\stackrel{\·\·}{v}+c\stackrel{\·}{v}+f_s=-m{\stackrel{\·\·}{v}}_g---\left(2\right)$

Wherein, m is non-resilient SDOF architecture quality, and c is non-resilient SDOF structure viscous damping coefficient, f _sfor non-resilient SDOF structure recovery power, for the second derivative of v, i.e. the acceleration response of non-resilient SDOF structure, for the first order derivative of v, i.e. the speed responsing of non-resilient SDOF structure, v is relative displacement, for v _gsecond derivative, i.e. earthquake ground motion acceleration, v _gfor seismic displacement;

The maximal value of relative displacement is maximum displacement response value, and hysteretic energy reacting value obtains by carrying out integral and calculating to relative displacement time-histories and restoring force time-histories, and earthquake motion finish time, corresponding integrated value was hysteretic energy reacting value;

The process of the related coefficient adopting amplitude modulation seismic motion record computation structure to react between amplitude modulation index is:

For any two vectorial X and Y, correlation coefficient value between the two can be calculated as follows:

$\mathrm{\ρ}(X,Y)=\frac{n\mathrm{\Σ}(X\·Y)-\mathrm{\Σ}X\·\mathrm{\Σ}Y}{\sqrt{(n\mathrm{\Σ}{\left(X\right)}^2-{\left(\mathrm{\Σ}X\right)}^2)\·(n\mathrm{\Σ}{\left(Y\right)}^2-{\left(\mathrm{\Σ}Y\right)}^2)}}---\left(3\right)$

Wherein n is earthquake motion number, vectorial X is set to the structural response value under 364 non-amplitude modulation earthquake motion effects, i.e. maximum displacement response or hysteretic energy reaction, and amplitude modulation Y being set to 364 non-amplitude modulation earthquake motions corresponding refers to target value;

Periodic regime 0.1 ~ 6.0s is divided into three constant time ranges, be respectively short period section 0.1 ~ 0.5s, short 0.6 ~ 1.5s of medium cycle and long period section 1.6 ~ 6.0s, first calculate related coefficient corresponding to each cycle respectively, then the weighting coefficient of three constant time ranges is weighted and on average obtains weighted mean related coefficient be the related coefficient between structural response and amplitude modulation index, by following formulae discovery:

${\stackrel{\‾}{\mathrm{\ρ}}}_w=\frac{1}{n_1\·n_2}{\mathrm{\Σ\ρ}}_{ij}\·w_j---\left(4\right)$

Wherein ρ _ijby according to formula (3) calculating i-th strength reduction factor and related coefficient corresponding to a jth structural cycle, n ₁for the number of strength reduction factor R, n ₂for the number of free vibration period of structure T, w _jfor the weight coefficient of a jth free vibration period of structure.

5. a kind of earthquake motion amplitude modulation index and amplitude modulation coefficient assessment method according to claim 4, is characterized in that: the weighting coefficient of described three constant time ranges is short period section is 4, and medium constant time range is 2, and long period section is 4/9.